Step-by-step explanation:
<h2><u>Given :-</u></h2>
(√3-√2)/(√3+√2)
<h2><u>To find :-</u></h2>
Rationalised form = ?
<h2><u>Solution:-</u></h2>
Given that
(√3-√2)/(√3+√2)
The denominator = √3+√2
The Rationalising factor of √3+√2 is √3-√2
On Rationalising the denominator then
=> [(√3-√2)/(√3+√2)]×[(√3-√2)/(√3-√2)]
=> [(√3-√2)(√3-√2)]×[(√3+√2)(√3-√2)]
=> (√3-√2)²/[(√3+√2)(√3-√2)]
=> (√3-√2)²/[(√3)²-(√2)²]
Since (a+b)(a-b) = a²-b²
Where , a = √3 and b = √2
=> (√3-√2)²/(3-2)
=> (√3-√2)²/1
=> (√3-√2)²
=> (√3)²-2(√3)(√2)+(√2)²
Since , (a-b)² = a²-2ab+b²
Where , a = √3 and b = √2
=> 3-2√6+2
=> 5-2√6
Hence, the denominator is rationalised.
<h2>
<u>Answer</u><u>:</u></h2>
Rationalised form of (√3-√2)/(√3+√2) is 5 - 2√6.
<h2><u>U</u><u>sed </u><u>formulae:</u><u>-</u></h2>
- (a+b)(a-b) = a²-b²
- (a-b)² = a²-2ab+b²
- The Rationalising factor of √3+√2 is √3-√2
